The use of nonlinear control methods in control engineering implies, in general, the knowledge of the full state vector. In this paper we present a nonlinear observer of reduced order (i.e. the order of the observer is less than the order of the nonlinear system observed) for estimating the state variables to be used in a trajectory tracking control loop. The nonlinear observer has the following characteristics : (1) the speed of convergence is adjustable; (2) the closed-loop control for trajectory tracking, with the observer in the loop, is stable. Applications to a robot arm and a neural network are included.